Characterizing the Age of Information with Multiple Coexisting Data Streams

Abstract

In this paper we analyze the distribution of the Age of Information (AoI) of a tagged data stream sharing a processor with a set of other data streams. We do so in the highly general setting in which the interarrival times pertaining to the tagged stream can have any distribution, and also the service times of both the tagged stream and the background stream are generally distributed. The packet arrival times of the background process are assumed to constitute a Poisson process, which is justified by the fact that it typically is a superposition of many relatively homogeneous streams. The first main contribution is that we derive an expression for the Laplace-Stieltjes transform of the AoI in the resulting GI+M/GI+GI/1 model. Second, we use stochastic ordering techniques to identify tight stochastic bounds on the AoI, leading to an explicit lower and upper bound on the mean AoI. In addition, when approximating the tagged stream's inter-generation times through a phase-type distribution (which can be done at any precision), we present a computational algorithm for the mean AoI. As illustrated through a sequence of numerical experiments, the analysis enables us to assess the impact of background traffic on the AoI of the tagged stream. It turns out that the upper bound on the mean AoI is remarkably close to its true value, which yields an explicit expression (in terms of the model parameters) for an accurate proxy of the AoI-minimizing generation rate.